RE: Data on N100 Stocks:
Oh goody, yummy yummy data! Thanx jperl. Now, lets look at the results of coin-toss, using the binomial distribution. You will find that the outcome of tossing a 50-50 coin 100 times looks nothing like the results of looking at N100 stocks over the last 100 days. The percentages of sequences with a particular number of "up-days" or "heads" falling within the same set of bins used by jperl is:
Range N100 Fair Coin
61-65 0.00% 1.67%
56-60 0.98% 11.80%
51-55 5.88% 32.46%
46-50 30.30% 35.57%
41-45 41.18% 15.57%
36-40 20.59% 2.67%
31-35 0.98% 0.17%
26-30 0.00% 0.00%
As you can see, the N100 results are heavily skewed toward too few "up-days." Whereas a sequence of 100 tosses of a fair coin would yield 56-60 heads in 11.8% of 100-toss sequences, the stocks on the N100 only saw 56-60 up-days in 0.98% of 100-day sequences. Likewise the N100 had too many sequences with very low numbers of heads. This bias in the distribution of reflects the bearish trend of the last 100 days and shows that if the N100 stocks are a coin-toss, they are certainly NOT a 50-50 coin toss.
Although it is a bit hard to judge the average number of up-days from this binned data, my guess is that it is around 44. The chance that 102 sequences of 100-tosses each of a fair coin would have an average of 44 heads per 100-toss sequence is extremely extremely low. Although the chance of a single 100-toss sequence have 44 or fewer heads is not low (having a probability of 13.6%), the chance that 102 sequences would have an average of 44 heads/sequence is extremely low (this is more than a 12-sigma event, having a probability on the order of 4xE-34). So, we can reject the hypothesis that the daily direction of movement of N100 stocks follows the same distribution as a 50-50 coin toss. (NOTE: this analysis only shows that the N100 is not a 50-50 fair coin, it could still be random with a more than 50% of a downday)
<b>RE: profitseer</b>
"Besides, the idea isn't to bet on the coin toss, the idea is to bet on how people will bet on a coin toss." -- profitseer
Beautifully said! This is why the markets are NOT random and why technical analysis works and why traders can profit. The price movement in the markets is determined by the actions of the buyers and sellers. And those buyers and sellers are not coin-tossers (OK, maybe some traders are coin-tossers!?), but human beings. As inandlong pointed out, human behavior follows predictable modes of fear, greed, and confusion that generate the bear, bull, and choppy price action respectively (as goldenarm mentioned).
The key is that price movements are NOT independent of each other the way coin tosses are. Although a coin is not aware that it flipped "tails" many times in row, the participants in the market are EXTREMELY and often painfully/joyfully aware of the number of downticks in a row and behave accordingly. Prior price action does influence the buyers and sellers, which does influence future price action.
With price movements being dependent on each other, the goal of the trader is to learn and exploit these dependencies. The challenge with trading is that the interdependencies between past and future price action are very complex (and partly driven by ostensibly random factors like news). Skilled traders learn to recognize the probable sentiment of the market and act accordingly.
So price movements are NOT independent of each other. Of course, once you lose the assumption of independence, you lose the central limit theorem, lose convergence to a normal distribution, lose all the nice statistic methods for predicting drawdown and optimizing bet size, etc. Much of the statistical analysis of the markets and trading is a real house of cards -- too much of it is based on assumptions which are too easily refuted.
Wishing everyone good & careful trading
-Traden4Alpha
Buying/selling and appearing to have no clue what they are doing, just "hoping"...